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Questions about concepts, definitions and distinctions

Does the concept apply to a particular case?

Given a tricky concept or definition, there are various types of question you can ask that check students' understanding of the concept. You can ask whether the concept or definition applies to a particular case. Here is an example, involving the concept of an argument:

Definition of argument: An argument consists of a conclusion along with one or more reasons for thinking that the conclusion is true.

Do the following passage contain arguments or not?

1. A number is said to be "prime' if it is divisible only by itself and one. The first five prime numbers are 2, 3, 5, 7 and 11. Long ago, Euclid proved that there is no end to the sequence of prime numbers – that is, for any prime number, there is a greater one.

A. Yes, the passage does contain an argument.

B. No, the passage does not contain an argument.

2. Capital punishment is justified if it deters people from committing violent crimes. However, the statistics on violent crime show that capital punishment does not act as a deterrent. Therefore, capital punishment is never justified.

A. Yes, the passage does contain an argument.

B. No, the passage does not contain an argument.

Consequences of definitions and concepts

More generally, you can ask about the logical consequences of definitions or concepts. For example, you can ask questions of the form: supposing this concept applies, what else can we infer? Here is an example involving the concept of having a right to something:

Suppose you intend to do X, and you discover that Bloggs has a right that you not do X. Which of the following is entailed by Bloggs's having that right?

A. You ought not to X.

B. You ought not to X without Bloggs's permission.

C. You may X provided you compensate Bloggs for any harm suffered as a result.

D. None of the above.

Questions about distinctions

Similar types of questions can be asked about distinctions - pairs of concepts that go together. For example, you can ask which of the two concepts applies to a particular example (or series of examples). Here is an example involving the distinction between intrinsic and relational properties:

For each of the following properties, are they intrinsic (A) or relational (B)?

  1. being taller than John Howard
  2. being a potential genius
  3. being 2 kg in weight
  4. being inside a womb

Here is a series of questions of the same form, concerning the distinction between deductive and inductive arguments:

For each of the following arguments, say whether they are (A) deductive or (B) inductive arguments:

  1. Alice must be an idiot because she smokes twenty cigarettes a day and only idiots smoke cigarettes.
  2. I picked an apple at random from Barrel "A'. But 98% of the apples in that barrel are red ones. So the apple I picked is probably red.
  3. Lions are carnivores and Bob is not a lion. So Bob is not a carnivore.
  4. About 50% of the population are male and 50% female. So about half of the nurses working in this hospital must be male.
  5. Either the witness is lying or the defendant is guilty. But we can be sure the witness is not lying, so the defendant is definitely guilty.
  6. I have just lost the last six hands of poker, so it's a dead certainty that I'll win the next one.

Here are some examples of True/False questions concerning the distinction between validty and soundness (truth of premises) for arguments:

1. If the conclusion of a valid argument is true, then all the premises must be true too.

A. True

B. False

2. A valid argument with a false conclusion cannot be sound.

A. True

B. False
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